A proof of Nielsen´s conjecture on the GPS dilution of precision

The dilution of precision terms for relative positioning are bounded from above by the corresponding dilution of precision terms for point positioning. This result is proven for the case of four satellites and conjectured to be valid for the case of more than four satellites. A proof of this conjecture is given. We also extend the result by giving two different lower bounds for the dilution of precision terms. The first lower bound depends on the receiver-satellite geometry, whereas the second does not. The proof of the bounds is based on the solution of a generalized eigenvalue problem